Exact ground states for the four-electron problem in a Hubbard ladder

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.Comment: 10 pages, 7 figure

Exact ground states for the four-electron problem in a two-dimensional finite Hubbard square system

We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works for arbitrary even particle number and lattice sites, is based on explicitly given symmetry adapted base vectors constructed in r-space. The Hamiltonian acting on these states generates a closed system of 85 linear equations providing by its minimum eigenvalue the exact ground state of the system. The presented results, described with the aim to generate further creative developments, not only show how the ground state can be exactly obtained and what kind of contributions enter in its construction, but emphasize further characteristics of the spectrum. On this line i) possible explications are found regarding why weak coupling expansions often provide a good approximation for the Hubbard model at intermediate couplings, or ii) explicitly given low lying energy states of the kinetic energy, avoiding double occupancy, suggest new roots for pairing mechanism attracting decrease in the kinetic energy, as emphasized by kinetic energy driven superconductivity theories.Comment: 37 pages, 18 figure

Discovery of the Onset of Rapid Accretion by a Dormant Massive Black Hole

Massive black holes are believed to reside at the centres of most galaxies. They can be- come detectable by accretion of matter, either continuously from a large gas reservoir or impulsively from the tidal disruption of a passing star, and conversion of the gravitational energy of the infalling matter to light. Continuous accretion drives Active Galactic Nuclei (AGN), which are known to be variable but have never been observed to turn on or off. Tidal disruption of stars by dormant massive black holes has been inferred indirectly but the on- set of a tidal disruption event has never been observed. Here we report the first discovery of the onset of a relativistic accretion-powered jet in the new extragalactic transient, Swift J164449.3+573451. The behaviour of this new source differs from both theoretical models of tidal disruption events and observations of the jet-dominated AGN known as blazars. These differences may stem from transient effects associated with the onset of a powerful jet. Such an event in the massive black hole at the centre of our Milky Way galaxy could strongly ionize the upper atmosphere of the Earth, if beamed towards us.Comment: Submitted to Nature. 4 pages, 3 figures (main paper). 26 pages, 13 figures (supplementary information